Polarizer-compensator-sample-analyzer

As another example of the use of the Poincare sphere, the relations for the case where the phase advancement along the fast axis of a wave plate, 5, is not exactly 90° (inexact quarter-wave plate) are worked out in the following. Here again the polarizer-compensator-sample-analyzer configuration is assumed. From Fig. A-3, the following identities are obtained ... 

Spectroscopic ellipsometers that measure A in the whole data range require an achromatic compensator with a phase shift close to 90° over a large spectral range. The compensator can be located between polarizer and sample or between sample and analyzer. 

When the sample is introduced between the polarizer and analyzer prism, optical rotation is produced, i.e., the plane polarized light emitted by the polarizer is rotated. The extent of rotation can be measured by rotating the analyzer with respect to the polarizer till the rotation is fully compensated. In more sophisticated instruments, a quartz-wave compensator is introduced. In these instruments, the polarizer and the analyzer are left permanently crossed... 

Figure 18-1. Geometry of standard null ellipsometer (a) and rotating analyzer ellipsometer (b). L, P, C, A, D and S represent the laser, polarizer, compensator, analyzer, detector and sample, respectively (after Jenkins, 1999).

With the compensator set for no compensation and (depending on the age of the microscope) and the polarizer and analyzer set for extinction, rotate the microscope stage, observing the intensity of light transmitted through the sample. A point of minimum intensity should easily be found (see Note 5). 

Figure 17.1.13 Schematic layout of one type of ellipsometer. Linearly polarized light (P) is incident on the sample (5). Reflection produces elliptic polarization (E), which is restored to linear polarization (A ) by the compensator (C). The analyzer (A) is adjusted to achieve extinction. [From R. H. Muller, Adv, Electrochem. Electrochem. Engr., 9, 167 (1973), with permission.]...

Figure 4.13. Experimental setup for the ellipsometric measurements 1. is a He-Ne laser, 2. is a chopper, 3. is a polarizer, 4. is a compensator, 5. is a sample chamber, 6. is an analyzer, and 7. is a detector (e.g., a photodiode). After [Yukioka and Inoue, 1991].

Several difl ereni types of cllipsometers arc available commercially. The earliest type was the null-type ellipsometer in which a circularly polarized incident beam was reflected off the sample surface onto an analyzer. The incident-beam polarization stale was chosen by a polarizer and compensator so that linearly polarized light was obtained after reflection. 1 he analyzer was then rotated until it was perpendicular to the polarization axis of the light coming from the sample as indicated by a minimum in the light iniciisiiy. Some instruments today still use the null principle, bui they are computer controlled and have charge-coupled-device (C (-I)f cameras as detectors. 

Birefringence can be measured directly, by measuring the two refractive indices of the sample and taking the difference, but this is usually inaccurate. Normally the specimen thickness and retardation are measured. Retardation is defined as [( i- M2)x(specimen thickness)] in nm, and is measured using a compensator, which is a crystal plate of known retardation. The specimen to be measured is set to the -45° position between crossed polars, and a compensator is inserted in its slot. This is above the specimen but below the analyzer at -f-45°. The compensator is adjusted until the specimen is dark, when its retardation is exactly cancelled by the compensator. If this adjustment is impossible, the sample must be rotated 90° to 4-45°. 

The layout of a typical ellipsometer is depicted in Fig. 4. The main components are a polarizer P which produces linearly polarized light, a compensator C which introduces a defined phase retardation of one field component with respect to the orthogonal one, the sample S, the analyzer A and a detector. 

This equation expresses the phase lag between x-axis polarization and y-axis polarization when the light passes through normal to the sample. The polarizer and analyzer are placed normal to each other. They are placed at 45° with respect to the x andy axes. Botii components deviate by b only when they pass through the sample. Figure 10 illustrates the principle of the measiuement. Babinet s compensator is positioned between the sample... 

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